As 3D images, hyperspectral images result in large sized data sets. The storage and transmission of large volumes of hyperspectral data have become significant concerns. Therefore efficient compression is required for storage and transmission. In this paper, a new hyperspectral remote sensing image compression method based on asymmetric 3D wavelet transform and 3D set partitioning scheme is proposed. Because most hyperspectral images have asymmetric statistical properties in all directions, an efficient asymmetric 3D wavelet transform (3DWT) is used to reduce redundancies in both the spectral and spatial dimensions. Compared with traditional symmetric 3D wavelet transform, asymmetric 3D wavelet transform can more efficiently remove the correlation between the adjacent bands. A modified 3DSPECK (3D set partitioning embedded block) algorithm, AT-3DSPECK (asymmetric transform 3DSPECK), is proposed and used to encode the transformed coefficients. According to the distribution of energy of the transformed coefficients, the 3D zeroblock partitioning algorithm and the 3D octave band partitioning scheme are efficiently combined in the proposed AT-3DSPECK algorithm. To accelerate the speed and optimize the rate-distortion performance of the embedded bit stream, a fast algorithm of the optimal zeroblock sorting is given. Experimental results show that the proposed algorithm outperforms AT-3DSPIHT (asymmetric transform 3D set partitioning in hierarchical trees) and 3DSPECK by 0.4 dB and 1.4dB on the average PSNR (peak signal to noise ratio) respectively. Compared with popular zerotree approaches, AT-3DSPECK is faster in coding speed.